Hannah is showing her work in simplifying (6.1 − 4.5) − 2.5 + 3.9. Identify any error in her work or reasoning.
Step 1: (6.1 − 4.5) − 2.5 + 3.9
Step 2: 6.1 + (− 4.5 − 2.5) + 3.9 (associative property)
Step 3: 6.1 − 7 + 3.9
Step 4: 6.1 + 3.9 − 7 (distributive property)
Step 5: 10 − 7 = 3
A. She wrote distributive instead of associative in Step 4.
B. She wrote associative instead of distributive in Step 2.
C. She wrote distributive instead of commutative in Step 4.
D. She wrote associative instead of commutative in Step 2.
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To identify any error in Hannah's work or reasoning, let's go through the steps she followed:
Step 1: (6.1 − 4.5) − 2.5 + 3.9
Step 2: 6.1 + (− 4.5 − 2.5) + 3.9 (associative property)
Step 3: 6.1 − 7 + 3.9
Step 4: 6.1 + 3.9 − 7 (distributive property)
Step 5: 10 − 7 = 3
Looking at the answer choices provided, we can see that the error is in Step 4. Hannah wrote "distributive" instead of the correct property, which is "commutative."
Therefore, the correct answer is:
C. She wrote distributive instead of commutative in Step 4.
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